Question

I’m confused on this one

Answer 1

The angles that form similarity are those that are vertically opposite and 2 pairs that are equal because the for a Z formation.

Since <LPM = <ONM then

$\dfrac{LP}{NO}=\dfrac{LM}{MO}\\ \\\dfrac{5x - 10}{4x-9}=\dfrac{16}{12}$ Cross multiply

12*(5x - 10) = 16*(4x - 9) Remove the brackets on both sides.

60x - 120 = 64x - 144 Subtract 60x from both sides.

- 120 = 64x - 60x - 144

-120 = 4x - 144 Add 144 to both sides.

-120 + 144 = 4x

24 = 4x Divide by 4

24/4 = x

x = 6